Rainbow Trees in Hypercubes
By: Nicholas Crawford , Maya Sankar , Carl Schildkraut and more
Potential Business Impact:
Finds hidden paths in computer networks.
We prove that every proper edge-coloring of the $n$-dimensional hypercube $Q_n$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_n$ can be properly edge-colored using only $n$ colors while avoiding rainbow cycles.
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